Slice selective MRI excitation with reduced power deposition using multiple transmit channels

ABSTRACT

Described are embodiments for slice-selective excitation for MRI that utilize multiple RF transmit coils, each of which are driven with a separate independent current waveform. These embodiments allow slice-selective excitation with slice profile and excitation time similar to other single-channel excitation, but with reduction in SAR caused by the transverse component of the RF field by a factor up to the number of excitation coils.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.12/398,982 filed Mar. 5, 2009, issued as U.S. Pat No. 8,169,219 on May1, 2012, which claims priority benefit of U.S. Provisional ApplicationNo. 61/034,113, filed Mar. 5, 2008, the entire contents of which areincorporated herein by reference.

GOVERNMENT LICENSE RIGHTS

The U.S. Government has a paid-up license in this invention and theright in limited circumstances to require the patent owner to licenseothers on reasonable terms as provided for by the terms of Grant No.CA112449-02 awarded by the National Institutes of Health.

FIELD OF THE INVENTIONS

This disclosure relates to magnetic resonance imaging (MRI), and inparticular to slice-selective excitation for MRI that utilizes multipleradio-frequency (RF) transmit coils.

BACKGROUND OF THE INVENTIONS

Magnetic resonance imaging (MRI) is a common modality for imaging jointsand other parts of the body due to its excellent definition ofligaments, cartilage, bone, muscle, fat and superior soft tissuecontrast. Many MR techniques have been able to provide information aboutlate stages of degeneration in which structural defects are present.

When a substance, such as human tissue, is subjected to a uniformmagnetic field, the individual magnetic moments of the spins in thetissue attempt to align with this polarizing field, but precess about itin random order at their characteristic Larmor frequency. If thesubstance, or tissue, is subjected to a magnetic field that is in thex-y plane, and which is near the Larmor frequency, the net alignedmoment, or “longitudinal magnetization,” may be rotated, or “tipped,”into the x-y plane to produce a net transverse magnetic moment. A signalis emitted by the excited spins after the excitation signal isterminated, and this signal may be received and processed to form animage.

When utilizing these signals to produce images, magnetic field gradientsare employed. Often, the region to be imaged is scanned by a sequence ofmeasurement cycles in which these gradients vary according to theparticular localization method being used. The resulting set of receivednuclear magnetic resonance (NMR) signals are digitized and processed toreconstruct the image using a reconstruction technique.

SUMMARY OF THE INVENTIONS

Disclosed are embodiments of slice selective excitation that utilizemultiple RF transmit coils. In some embodiments, each coil is driven bya separate independent control channel, which achieves slice selectionwith markedly decreased specific absorption rate (SAR), which is ameasure of patient heating. Reduced SAR is achieved, in embodimentsdescribed herein, with little or no change in slice profile and littleor no significant increase in excitation time.

In some embodiments, methods and apparatus are described for reducing aspecific absorption rate (SAR) over a field of view of an imaged objectduring magnetic imaging (MRI). Some embodiments include the steps ofemitting a first radiofrequency (RF) pulse into an object with an RFexcitation coil element that has a first sensitivity profile comprising(a) a substantially uniform amplitude, and (b) a first phase that issubstantially constant in a direction across an imaging volume of theobject; emitting a second RF pulse into the object with a second RFexcitation coil element that has a second sensitivity profile comprising(a) a substantially uniform amplitude, and (b) a second phase thatvaries substantially linearly, with a first nonzero integer multiple of2π phase variation, in the direction across the imaging volume; andemitting a third RF pulse into the object with a third RF excitationcoil element that has a third sensitivity profile comprising (a) asubstantially uniform amplitude and (b) a third phase that variessubstantially linearly, with a second nonzero integer multiple of −2πphase variation, in the direction across the imaging volume.

In some embodiments, an improved SAR, resulting from emission of thefirst, second, and third RF pulses over a field of view of the object,is decreased relative to an unimproved SAR, resulting from emission of afourth RF pulse that would produce substantially the same amount oftransverse magnetization as emission of the first, second, and third RFpulses over the field of view.

Some embodiments provide that RF pulses are emitted into the object by nRF coil elements, and in certain embodiments, n≧3. In some embodiments,the improved SAR is reduced by about a factor of n relative to theunimproved SAR. In some embodiments, the first and second nonzerointegers are positive integers. Some embodiments provide that the firstand second nonzero integers are the same positive integer. In certainembodiments, the first phase is substantially zero across the imagingvolume. In some embodiments, each of the first, second, and third RFpulses comprises a waveform that is substantially identical in shape to,but shifted in time relative to, each of the others of the first,second, and third waveforms.

Some embodiments provide methods for reducing a specific absorption rate(SAR) over a field of view of an imaged object during magnetic imaging(MRI) that include emitting a first radiofrequency (RF) pulse into anobject with an RF excitation coil element that has a first sensitivityprofile comprising a first phase that is substantially constant acrossan imaging volume of the object; emitting a second RF pulse into theobject with a second RF excitation coil element that has a secondsensitivity profile comprising a second phase that varies substantiallylinearly, with a first nonzero integer multiple of 2π phase variation,in a direction across the imaging volume; and emitting a third RF pulseinto the object with a third RF excitation coil element that has a thirdsensitivity profile comprising a third phase that varies substantiallylinearly, with a second nonzero integer multiple of −2π phase variation,in the direction across the imaging volume.

In some embodiments, an improved SAR, resulting from emission of thefirst, second, and third RF pulses over a field of view of the object,is decreased relative to an unimproved SAR, resulting from emission of afourth RF pulse that would produce substantially the same amount oftransverse magnetization as emission of the first, second, and third RFpulses over the field of view.

In some embodiments, RF pulses are emitted into the object by n RF coilelements, and in certain embodiments, n≧3. In some embodiments, RFpulses are transmitted via n RF channels, and in certain embodiments,n≧3. Some embodiments provide that the improved SAR varies spatiallyacross the field of view. In some embodiments, the improved SAR isreduced by about a factor of n relative to the unimproved SAR.

Some embodiments provide that the first and second nonzero integers arepositive integers. In some embodiments, the first and second nonzerointegers are the same positive integer. In certain embodiments, thefirst phase is substantially zero across the imaging volume. Someembodiments, provide that each of the first, second, and third RF pulsescomprises a waveform that is substantially identical in shape to, butshifted in time relative to, each of the others of the first, second,and third waveforms.

Some embodiments described herein relate to a system, for reducing aspecific absorption rate (SAR) over a field of view of an imaged objectduring magnetic imaging (MRI), that includes a transmit module. In someembodiments, the transmit module is programmed to emit a firstradiofrequency (RF) pulse into an object with an RF excitation coilelement that has a first sensitivity profile comprising a first phasethat is substantially constant across an imaging volume of the object;emit a second RF pulse into the object with a second RF excitation coilelement that has a second sensitivity profile comprising a second phasethat varies substantially linearly, with a first nonzero integermultiple of 2π phase variation, in a direction across the imagingvolume; and emit a third RF pulse into the object with a third RFexcitation coil element that has a third sensitivity profile comprisinga third phase that varies substantially linearly, with a second nonzerointeger multiple of −2π phase variation, in the direction across theimaging volume. In some embodiments, an improved SAR, resulting fromemission of the first, second, and third RF pulses over a field of viewof the object, is decreased relative to an unimproved SAR, resultingfrom emission of a fourth RF pulse that would produce substantially thesame amount of transverse magnetization as emission of the first,second, and third RF pulses over the field of view.

For purposes of summarizing the disclosure, certain aspects, advantages,and novel features of the disclosure have been described herein. It isto be understood that not necessarily all such advantages may beachieved in accordance with any particular embodiment of the disclosure.Thus, the disclosure may be embodied or carried out in a manner thatachieves or optimizes one advantage or group of advantages as taughtherein without necessarily achieving other advantages as may be taughtor suggested herein.

BRIEF DESCRIPTION OF THE DRAWINGS

General descriptions provided herein that implement various features ofthe disclosure will now be described with reference to the drawings. Thedrawings and the associated descriptions are provided to illustrateembodiments of the disclosure and not to limit the scope of thedisclosure.

FIG. 1A depicts a RF envelope and z gradient current waveforms of aslice-selective excitation.

FIG. 1B depicts a slice profile in z, assuming uniform RF coilsensitivity.

FIG. 1C depicts the SAR resulting from the transverse component of B1.

FIG. 2 depicts a coil sensitivity profile phase for a 3-coil embodiment.

FIG. 3A depicts embodiments of slice selection with a 3-channel system,showing RF waveforms for each of the three channels.

FIG. 3B depicts embodiments of slice selection with a 3-channel system,showing transverse magnetization achieved by the 3-channel system.

FIG. 3C depicts embodiments of slice selection with a 3-channel system,showing SAR from transverse component of B1 for the 3-channel system.

FIG. 4A depicts RF and gradient waveforms for a slice selectiveexcitation for a thick slice with width one-half the field of view.

FIG. 4B depicts achieved transverse magnetization for a slice selectiveexcitation for a thick slice with width one-half the field of view.

FIG. 4C depicts relative SAR for a slice selective excitation for athick slice with width one-half the field of view.

FIG. 5A depicts RF and gradient waveforms of a reduced SAR sliceselection for a thick slice with a width one-half the field of view, andwith a 3-channel system.

FIG. 5B depicts achieved transverse magnetization of a reduced SAR sliceselection for a thick slice with a width one-half the field of view, andwith a 3-channel system.

FIG. 5C depicts relative SAR arising from the transverse component of B1of a reduced SAR slice selection for a thick slice with a width one-halfthe field of view, and with a 3-channel system.

FIG. 6 depicts a k-space representation of 3-channel excitation.

FIG. 7A depicts a 3-channel excitation of an off-isocenter axial slice,showing transverse magnetization achieved by 3-channel excitation ofoff-isocenter slice modulate ¼ field of view to the left.

FIG. 7B depicts relative SAR due to transverse B1.

FIG. 8A, depicts RF waveforms 1 through 8 designed for coil sets forembodiments of slice selective excitation with 8 RF channels.

FIG. 8B depicts the transverse magnetization for embodiments of sliceselective excitation with 8 RF channels.

FIG. 8C depicts SAR for the 8-channel system integrated over the fieldof view.

FIG. 9 depicts a 3-coil excitation of an off-axial slice visualized inexcitation k-space.

FIG. 10 depicts the performance of multiple coil excitation foroff-axial slices.

FIG. 11A depicts the magnitude of excitation profile in the in-slicedirection.

FIG. 11B depicts the transverse SAR in connection with embodimentsdepicted in FIG. 11A.

FIG. 12 depicts a schematic representation of an MRI transmit module inaccordance with embodiments described herein.

DETAILED DESCRIPTION OF THE INVENTIONS

Described herein are embodiments for slice-selective excitation for MRIthat utilize multiple RF transmit coils, each of the coils being drivenwith a separate independent current waveform. These embodiments allowslice-selective excitation with slice profile and excitation timesimilar to conventional single-channel excitation but with reduction inSAR caused by the transverse component of the RF field by a factor up tothe number of excitation coils.

Results described herein are based on numerical integration of the Blochequation, neglecting T1 and T2 relaxation. Transverse SAR was calculatedby summing over time the square amplitude of the transverse component ofthe RF field B1 at each spatial location, which depends on theindividual RF waveforms and coil sensitivity profiles.

Conventional Slice-Selective Excitation

Slice-selective excitation is achieved by applying a current to the RFexcitation coil which is modulated at the proton resonant frequency (64MHz for a 1.5 Tesla main field strength), with a time envelope which isapproximately equal to the Fourier transform of the desired sliceprofile. A constant gradient field is applied during the excitationprocess. The direction of the gradient determines the orientation of theselected slice, and the gradient strength determines the thickness ofthe slice profile. Excitation is typically performed with a coildesigned for optimal field uniformity.

FIGS. 1A-1C depict a conventional slice-selective excitation. FIG. 1Adepicts RF envelope and z gradient current waveforms. The RF envelopewas designed by Fourier transform with Hamming window. FIG. 1B depicts aslice profile in z, assuming uniform RF coil sensitivity. Units arefraction of maximum possible transverse magnetization M_(zo). FIG. 1Cdepicts the SAR resulting from the transverse component of B1. Forconventional slice selection, the SAR is constant across the field ofview, whether in or out of slice.

With a substantially uniform RF field, the SAR of a conventionalslice-selective pulse is the same over the entire sensitive volume ofthe coil. Areas both within and without the selected slice experiencethe same RF field strength over time, and hence the same SAR, but thetime sequence of tips adds to zero in areas outside the selected sliceand adds to the desired flip angle in areas within the slice.

FIGS. 1A-1C illustrates conventional slice-selective excitation. FIG. 1Ashows an RF time envelope and gradient current waveform. The RF waveformwas designed by Fourier transform and has the form of a sine functionmultiplied by a Hamming window function. The waveform is scaled for a90° flip angle. FIG. 1B shows the resulting transverse magnetization inits components Mx and My achieved by this excitation if performed withan RF coil having uniform amplitude and constant phase sensitivityprofile. Units are in fraction of the equilibrium longitudinalmagnetization M_(zo). The non-zero value of Mx within the slice profileis a consequence of violation of the low-flip angle assumption uponwhich RF design by Fourier transform is based, and is generic to any RFpulse designed by the Fourier transform method. FIG. 1C shows the SARdue to the component of B1 in the transverse x-y plane. SAR due to B1 inthe z axis is not considered. Units of SAR in FIG. 1C are arbitrary.

Slice-Selective Excitation with Multiple Coils

When multiple RF coils are used, a pattern of destructive andconstructive interference of the RF fields from each coil can result indecreased SAR in some regions of the imaging volume. With appropriatelydesigned RF coils, RF coil current waveforms, and gradient waveforms,slice selective excitation can be achieved with greatly reduced SAR. Asused herein, the term “coil element” is a broad term and can refer to anRF coil or a component of an RF coil that sends an RF signal via an RFchannel. In some embodiments, an RF coil may comprise multiple RF coilelements.

SAR reduction is obtained by a factor of 3 for a system of threeindependent RF current sources and three different RF coils. Theunderlying principle may be extended to any number of coils and RFchannels, with SAR reduction factor up to the number of coils andchannels.

FIG. 2 depicts a coil sensitivity profile phase for a 3-coil embodiment.Coil 1 has a constant sensitivity amplitude and a zero phase. Coil 2 hasa constant amplitude but a phase which varies linearly in z. Coil 3 hasa constant amplitude but a phase which varies inversely linearly in z.Coil amplitude and phase refer to amplitude and phase in the x-y plane,neglecting the RF field in the z direction (B1 z), which does notcontribute to excitation. B1 z does contribute to SAR, and minimizationof B1 z can be a goal of coil design.

In some embodiments, a set of RF coils that can be designated as a“linear phase” coil configuration. In this configuration, one coil has asensitivity profile with a uniform amplitude and a constant phase acrossthe imaging volume. The second coil has a uniform amplitude but a phasethat varies linearly in a single direction with a total of 2π phasevariation across the imaging volume. The third coil has a uniformamplitude but a phase that varies linearly in the same direction with atotal variation of −2π radians. The phase of the coil sensitivityprofile for these three coils is illustrated in FIG. 2. Forconcreteness, the direction of phase variation can be considered to bethe z axis, the direction of the main field. Phase variation in anydirection could be used with the proposed method of slice selection. Thez axis can be selected, in some embodiments, for concrete illustrationbecause coil designs exist which give the desired coil sensitivity withnearly uniform amplitude and with linear phase distribution along the zaxis. One physical realization of such an RF coil set would be a set ofthree birdcage coils which are arranged coaxially along the z axis, withthe second coil twisted to give +2π radians phase variation across the zfield of view, and the third coil twisted to give −2π radians phasevariation across the z field of view. A twisted birdcage coil havingsuch a linear phase property has been described in Alsop D C, Connick TJ, Mizsei G., A spiral volume coil for improved RF field homogeneity athigh static magnetic field strength, Magn Reson Med 1998; 40(1):49-54,the entirety of which is incorporated herein and made a part of thisspecification. An alternative physical realization would consist ofcoaxial birdcage coils with an external shield separated from thebirdcage rungs by a dielectric, as described in Foo T K, Hayes C E, KangY W, Reduction of RF penetration effects in high field imaging, MagnReson Med 1992; 23(2):287-301, the entirety of which is incorporatedherein and made a part of this specification.

In this context, the phase and amplitude referred to are of thecomponent of the coil sensitivity profile which lies in the transversex-y plane of the MRI system, i.e. the plane perpendicular to the mainfield. The z component of the RF coil sensitivity profile is neglected.The z component of the RF field does not contribute to excitation, butis a source of SAR. Coil design optimization can be performed tominimize the z component of the RF field. Reduction in SAR with thecurrent method refers only to the component of SAR related to the RFfield in the transverse x-y plane.

The RF waveforms for all three coils are calculated independently as ifthe coils were to be used singly to achieve a conventional sliceselective excitation. One example of a suitable RF waveform designprocess would be the Fourier transform method. The RF waveform for thesecond coil (with +2π linear phase) is designed by replicating the RFwaveform of coil 1, but shifting it in time. The time shift length ischosen so that the amount of linear phase which accumulates during theinterval due to the gradient field is equal to the linear phase of theRF coil. Specifically, if a given coil has linear phase of 2nπ acrossthe FOV, the time shift Δt of the RF waveform for this coil relative tothe RF waveform of the coil with constant phase (designated coil 1 inour concrete 3-coil scenario) isΔt=2nπ/γG  (1.1)where G is the gradient strength of the slice-select gradient (Gz in ourimplementation) and γ is the gyromagnetic ratio in units of radians perunit gradient strength.

Similarly, the RF waveform for the third coil is shifted by acorresponding time increment which, for this particular coilconfiguration, will be the negative of the time shift of the secondcoil's waveform. Finally, the amplitude of each RF waveform ismultiplied by a factor of ⅓. The resulting RF current waveforms for eachof the three channels are shown in FIG. 3A.

FIGS. 3A-3C depict a slice selection with a 3-channel system. FIG. 3Adepicts RF waveforms for each of the three channels. Each waveform isscaled by ⅓ compared to the single channel waveform of FIG. 1A. Thewaveform for channel 2 lags the waveform for channel 1 by Δt. Thewaveform for channel 3 leads the waveform for channel 1 by Δt. Thegradient waveform is unchanged from the single channel case of FIG. 1A.FIG. 3B depicts transverse magnetization achieved by the 3-channelsystem. This is essentially identical to that achieved by the singlechannel system shown in FIG. 1B. FIG. 3C depicts SAR from transversecomponent of B1 for the 3-channel system. Unlike the single channelsystem, SAR for the three channel system is a function of location inthe z direction. Units are arbitrary, but are the same as in FIG. 1C forcomparison. Total SAR over the field of view is ⅓ that of the SAR forthe single channel system.

The achieved transverse magnetization Mxy resulting from the 3-channelexcitation scheme is shown in FIG. 3B. The excited slice profile isnearly identical to that achieved by a conventional single channelexcitation shown in FIG. 1B. FIG. 3C shows the SAR due to the componentof B1 in the x-y plane. Unlike SAR with a conventional one-channel sliceselective excitation, SAR in the 3-channel system has a spatialvariation. Units in FIG. 3C are arbitrary, but are the same as in FIG.1C for accurate comparison. SAR for the 3-channel system is equal to orlower than SAR for the two-channel system at every point in the imagingfield of view (FOV). SAR averaged over the entire FOV is decreased inthe 3-channel excitation by a factor of 3.

FIGS. 4A-4C depict a conventional slice selective excitation for a thickslice with width one-half the field of view, with FIG. 4A depicting RFand gradient waveforms, FIG. 4B depicting achieved transversemagnetization, and FIG. 4C depicting relative SAR.

FIGS. 5A-5C depict a reduced SAR slice selection for a thick slice witha width one-half the field of view, with a 3-channel system. FIG. 5Adepicts RF and gradient waveforms. The time offset Δt is calculatedaccording to Equation (1.1) and is greater than for the thin sliceselection of FIG. 3. FIG. 5B depicts achieved transverse magnetization,which is essentially the same as for the single channel system of FIGS.4A-4C. FIG. 5C depicts relative SAR arising from the transversecomponent of B1. Units are arbitrary, but are the same as for FIGS.4A-4C to allow comparison. SAR integrated over the FOV is ⅓ that of thesingle transmitter system.

RF waveforms and excitation results for conventional single-channelexcitation and the 3-coil system are presented in FIGS. 4A-4C and 5A-5Cfor a slice thickness equal to one half the imaging field of view. Suchexcitation might be used for slab selective excitation for 3-dimensionalimaging. Although the shape of the SAR distribution across the imagingFOV varies with slice thickness, the factor of transverse SAR reductionis independent of slice thickness. For a given RF waveform, slicethickness is increased by decreasing gradient amplitude. This results ina longer delay time Δt, according to Equation (1.1), which isillustrated in FIG. 5A.

This method can be extended to any number of RF channels, eachcontrolling current through a coil with linear phase distribution with adifferent multiple of 2π phase variation across the imaging field ofview. Slice profiles nearly identical to the single-channel case areobtained with transverse SAR reduction factor equal to the number ofchannels.

FIG. 6 depicts a k-space representation of 3-channel excitation. Eachcoil represents a point in excitation k-space. The distance Δk betweenpoints represents the linear phase in the sensitivity profile of eachcoil, in units of excitation k-space (i.e. cycles/cm). The dotted lineshows the trajectory through excitation k-space traversed by the zgradient. The initial left-to-right path corresponds to the positivegradient lobe. The subsequent right-to-left path corresponds to thenegative gradient refocusing lobe. The excitation from all three coilstraverse the same k-space trajectory in tandem.

Insight into this excitation scheme may be gained by considering theexcitation in k-space. As illustrated in FIG. 6, the three coilscorrespond to three points in excitation k-space. When the gradient isturned on and excitation begins, the excitation k-space is traversed. Ifeach coil is to produce an identical slice profile, the same excitationk-space must be scanned by each coil. This is achieved by making the RFwaveforms the same but shifted in time relative to each other. The timeshift for each coil's RF waveform (relative to the constant phase coil,coil number 1) depends on the speed of k-space traversal (i.e., gradientstrength) and on the separation of the three points in excitationk-space (i.e., the amount of linear phase incorporated into each RFcoil).

FIGS. 7A-7B depict a 3-channel excitation of an off-isocenter axialslice. Movement of the slice profile off-isocenter is achieved bymodulating the RF waveforms by the appropriate frequency, as inconventional slice selective excitation. For this example, this wasaccomplished by adding the appropriate phase to each point of the RFtime envelope. FIG. 7A depicts transverse magnetization achieved by3-channel excitation of off-isocenter slice modulated ¼ FOV to the left.FIG. 7B depicts relative SAR due to transverse B1. The SAR profileshifts with the slice. Total SAR across the imaging FOV is reduced by ⅓,which is the same as for the unshifted case.

The slice selective transmit SENSE excitation can be modulated to anoff-isocenter slice location by modulation frequency offset of the RFwaveforms in the same manner used for off-isocenter selection of aconventional slice selective excitation. Modulation off-isocenter causesno change in the performance of the method and no change in SARreduction. The spatial SAR profile shifts along with the slice profilewhen the center frequency of the RF waveform is changed. This isillustrated in FIGS. 7A-7B.

FIGS. 8A-8C depict slice selective excitation with 8 RF channels. FIG.8A depicts RF waveforms 1 through 8 designed for coil sets having 0, 2π,−2π, 4π, −4π, 6π, −6π, and 8π linear phase respectively. FIG. 8B depictsthat the slice profile achieved is essentially identical to thatachieved by single channel system. FIG. 8C depicts that the SAR for the8-channel system integrated over the field of view is ⅛ that of thesingle channel system.

The method can be extended to any number of channels, with decrease inSAR by a factor of the number of channels. FIGS. 8A-8C shows results foran eight-channel system, with coils varying from −6π phase through 8πlinear phase over the imaging volume, for a slice thickness 1/16th thefield of view. In general, the degree of SAR decrease integrated overthe coil volume is proportional to the number of channels and isunaffected by the slice thickness of the excitation. The shape of theSAR distribution changes with slice thickness, as illustrated in FIGS.3A-3C and 4A-4C, and with the number of channels, as illustrated byFIGS. 3A-3C and 8A-8C.

Performance for Off-Axial Slices

The above description is based on slice selection in a planeperpendicular to the direction of phase variation of the RF coilelements. For a twisted birdcage coil oriented along z, this correspondsto excitation of an axial slice, i.e. in the x-y plane. If the desiredexcitation is in a plane outside the true axial plane, the performanceof the method changes. The degree of SAR decrease remains unchanged, butthe slice flip angle profile becomes modulated by a sinusoidal functionin one in-slice direction. For a two coil system, this modulation has acosine form. For more coils, the modulation becomes a more complexsummation of sinusoids.

FIG. 9 depicts a 3-coil excitation of an off-axial slice visualized inexcitation k-space. As in the axial slice case, the three coilsrepresent three points in excitation k-space. Unlike the axial slicecase, the excitation k-space trajectories traversed by each coil foroff-axial slice excitation are not collinear.

Insight into the performance of the method for off-axial slices can begained by considering the coil configuration in excitation k-space. Thisis illustrated for a 3-coil configuration in FIG. 9. For example,illustrated is the case of 30° rotation of the slice toward the plane ofconstant y. This is achieved by playing the gradient waveform out overboth the z and y gradient coils simultaneously, appropriately weightedto give the correct rotated gradient direction and amplitude. Althoughillustrated for a single off-axial plane, the following analysis of theperformance of the multiple coil slice selection method applies to anyoff-axial plane.

The three coils correspond to three points in excitation k-space, thesame as in the axial slice case. In the axial slice case, the k-spacetrajectory was only along the z axis, and all three coils depositedexcitation k-space energy along the z axis only, resulting in a onedimensional excitation k-space and a resulting excitation which wasselective only in z, and constant in x and y. For the off-axial slicecase, the excitation becomes two dimensional, as the k-spacetrajectories of the individual coils are no longer along the same line.The resulting excitation will be selective in two dimensions (z and y inthe particular case illustrated in FIG. 9).

RF waveforms are designed for the off-axial slice case in the same wayas for the axial slice, but with a different time offset Δt between thewaveforms given now byΔt=2nπ cos θ/γG  (1.2)where θ is the angle between the selected slice and the axial plane.Equation (1.2) for the off-axial plane differs from Equation (1.1) forthe axial plane by the factor cos θ.

FIG. 10 depicts the performance of multiple coil excitation foroff-axial slices. Results are shown for a three-coil system, with RFwaveforms equally weighted. The top row of FIG. 10 shows a magnitude oftransverse magnetization as a function of location in z and y forvarious values of θ, the angle of the slice plane with respect to thex-y plane. Slice profile is graphed along three lines labeled 1, 2, and3 representing the slice profile at isocenter (1), the slice profile ¼FOV away from isocenter (2), and along the in-slice direction (3). Sliceprofile at isocenter remains unchanged at any off-axial angle θ. Sliceprofile away from isocenter decreases, in magnitude but retains the sameshape as at isocenter. Note that variation in slice profile magnitudeoccurs in one in-slice direction (y in this case). There is no variationin the other in-slice dimension (x in this case). Slice profile remainsnearly unchanged for off-axial angles up to 30°. SAR reduction by ⅓remains the same for any off-axial angle θ.

Simulation results are shown in FIG. 10 for the magnitude of thetransverse magnetization achieved by the 3-coil system for variousvalues of θ, i.e. slice planes with various angles from the axial plane.For all of these values of θ, the transverse SAR reduction factor of 3is unchanged. However, for larger values of θ the modulation of themagnitude of the slice profile in one in-plane direction increases. Theslice profile in the orthogonal in-slice direction remains constant. Forthe results shown in FIG. 10, the RF waveforms are all of the samemagnitude.

In the example shown in FIG. 10, equal weighting of the three RFwaveforms gives a modulation of the slice profile as a function ofdistance r from isocenter along one in-slice direction by a functionm(r)=1+2 cos(2πrΔk sin θ)  (1.3)where Δk is the distance between k-space points representing each coil,as defined in FIG. 6.

Modulation of the slice profile magnitude occurs in one in-slicedirection, and the slice profile remains constant in the orthogonalin-slice dimension. m(r) represents the Fourier transform of theexcitation k-space along a line orthogonal to the k-space path definedby the constant slice select gradient. In particular, m(r) given inEquation (1.3) represents the Fourier transform of the functionδ(k)+δ(k−Δk sin θ)+(k+Δk sin θ)  (1.4)which reflects the equal weighting of the three RF waveforms. We denotethis weighting scheme as “1-1-1.” Different weighting of the RFwaveforms will give different shape to m(r), which may be optimized forparticular imaging situations.

FIGS. 11A-11B depict the effect of nonuniform weighting of the RFwaveforms for a 3-channel system for a 30° off-axial slice. FIG. 11Adepicts the magnitude of excitation profile in the in-slice direction(equivalent to line 3 in FIG. 10) showing modulation of the excitationamplitude. More uniform excitation is achieved with the 1-2-1 RFwaveform weighting scheme (coil 1 waveform has twice the amplitude ofcoils 2 and 3) than with the 1-1-1 scheme (all RF waveforms are equal inamplitude). FIG. 11B depicts transverse SAR. Total SAR for the 1-2-1scheme is 0.375 times the SAR of a single channel excitation, whiletotal SAR for the 1-1-1 scheme is 0.333 times the single channel SAR.SAR reduction can be traded off for improved homogeneity of sliceprofile for off axial slices by adjusting the weighting of the RFwaveforms, in this 3-channel example or with any number of channels.Maximum SAR reduction occurs when RF waveforms are equally weighted.

FIGS. 11A-11B show the results of excitation with the RF waveform ofcoil 1 weighted with twice the magnitude of the RF waveforms of coils 2and 3, with waveforms renormalized to still give 90° flip angle. Thecorresponding k-space sampling function becomes

$\begin{matrix}{{\delta(k)} + {\frac{1}{2}{\delta\left( {k - {\Delta\; k\;\sin\;\theta}} \right)}} + {\frac{1}{2}{\delta\left( {k + {\Delta\; k\;\sin\;\theta}} \right)}}} & (1.5)\end{matrix}$which leads to a modulation functionm(r)=1+cos(2πrΔk sin θ)  (1.6)This scheme is denoted “1-2-1” in FIGS. 11A-11B.

FIGS. 11A-11B show that the uniformity of slice profile magnitude isimproved with the 1-2-1 weighting, at the expense of slightly less SARreduction. SAR for the 1-1-1 weighting is ⅓ that of single channelexcitation, while SAR for the 1-2-1 scheme is 0.375 that of the singlechannel excitation. This example shows that SAR reduction can beflexibly traded off with slice profile uniformity for off-axial slicesby adjusting the relative weighting of the different coil RF waveforms.With a large number of channels, the waveform design problem becomes atrue two-dimensional Fourier transform design problem, for which anarbitrary in-plane slice profile can be prescribed. However, maximum SARreduction is achieved when the amplitude of the individual channel RFwaveforms is equal.

Described herein is a method of slice selection which utilizes multipletransmit channels to achieve slice profiles identical to those obtainedby conventional single transmit channel slice selective pulses, in thesame excitation time, but with dramatic reduction of SAR by a factor upto the number of transmit channels. The transverse component of SAR isreduced by destructive interference of the RF excitation at locationsoutside the selected slice.

This method is presented for hypothetical coil sensitivity profileswhich are constant in amplitude but with linearly varying phase. Suchcoil sensitivity profiles may be possible with twisted birdcage coildesigns.

FIG. 12 depicts a system, for reducing a specific absorption rate (SAR)over a field of view of an imaged object during magnetic imaging (MRI),that includes a transmit module. In some embodiments, the transmitmodule is programmed to emit a first radiofrequency (RF) pulse into anobject with an RF excitation coil element that has a first sensitivityprofile comprising a first phase that is substantially constant acrossan imaging volume of the object; emit a second RF pulse into the objectwith a second RF excitation coil element that has a second sensitivityprofile comprising a second phase that varies substantially linearly,with a first nonzero integer multiple of 2π phase variation, in adirection across the imaging volume; and emit a third RF pulse into theobject with a third RF excitation coil element that has a thirdsensitivity profile comprising a third phase that varies substantiallylinearly, with a second nonzero integer multiple of −2π phase variation,in the direction across the imaging volume. In some embodiments, animproved SAR, resulting from emission of the first, second, and third RFpulses over a field of view of the object, is decreased relative to anunimproved SAR, resulting from emission of a fourth RF pulse that wouldproduce substantially the same amount of transverse magnetization asemission of the first, second, and third RF pulses over the field ofview.

Although preferred embodiments of the disclosure have been described indetail, certain variations and modifications will be apparent to thoseskilled in the art, including embodiments that do not provide all thefeatures and benefits described herein. It will be understood by thoseskilled in the art that the present disclosure extends beyond thespecifically disclosed embodiments to other alternative or additionalembodiments and/or uses and obvious modifications and equivalentsthereof. In addition, while a number of variations have been shown anddescribed in varying detail, other modifications, which are within thescope of the present disclosure, will be readily apparent to those ofskill in the art based upon this disclosure. It is also contemplatedthat various combinations or subcombinations of the specific featuresand aspects of the embodiments may be made and still fall within thescope of the present disclosure. Accordingly, it should be understoodthat various features and aspects of the disclosed embodiments can becombined with or substituted for one another in order to form varyingmodes of the present disclosure. Thus, it is intended that the scope ofthe present disclosure herein disclosed should not be limited by theparticular disclosed embodiments described above.

1. A method, of emitting radio frequency (RF) pulses into an objectduring magnetic resonance imaging (MRI), comprising: emitting a first RFpulse into the object with a first RF excitation coil element, whereinthe first RF pulse comprises a first RF waveform; emitting a second RFpulse into the object with a second RF excitation coil element, whereinthe second RF pulse comprises a second RF waveform that is time shiftedrelative to the first RF waveform by 2nπ/γG, where G is a gradientstrength of a slice-select gradient, γ is a gyromagnetic ratio in unitsof radians per unit gradient strength, and n is an integer; and emittinga third RF pulse into the object with a third RF excitation coilelement, wherein the third RF pulse comprises a third RF waveform thatis time shifted relative to the first RF waveform by −2nπ/γG.
 2. Themethod of claim 1, wherein RF pulses are emitted into the object by n RFcoil elements.
 3. The method of claim 2, wherein n≧3.
 4. The method ofclaim 1, wherein the first, second and third RF waveforms aresubstantially identical in shape.
 5. The method of claim 1, furthercomprising, after emitting the third RF pulse, detecting an RF signalscattered from the object for generating an MRI image.
 6. The method ofclaim 1, wherein the first RF excitation coil element has a firstsensitivity profile comprising a first phase that is substantiallyconstant in a direction across an imaging volume of the object, thesecond RF excitation coil element has a second sensitivity profilecomprising a second phase that varies substantially linearly, with an nmultiple of 2π, in the direction across the imaging volume, and thethird RF excitation coil element has a third sensitivity profilecomprising a third phase that varies substantially linearly, with an nmultiple of −2π, in the direction across the imaging volume.
 7. Themethod of claim 6, wherein the first phase is substantially zero acrossthe imaging volume.
 8. The method of claim 6, wherein the sensitivityprofile of each of the first, second and third excitation coil elementscomprises a substantially uniform amplitude across the imaging volume.9. A system, for emitting radio frequency (RF) pulses into an objectduring magnetic resonance imaging (MRI), comprising: a transmit module,programmed to: emit a first RF pulse into the object with a first RFexcitation coil element, wherein the first RF pulse comprises a first RFwaveform; emit a second RF pulse into the object with a second RFexcitation coil element, wherein the second RF pulse comprises a secondRF waveform that is time shifted relative to the first RF waveform by2nπ/γG, where G is a gradient strength of a slice-select gradient, γ isa gyromagnetic ratio in units of radians per unit gradient strength, andn is an integer; and emit a third RF pulse into the object with a thirdRF excitation coil element, wherein the third RF pulse comprises a thirdRF waveform that is time shifted relative to the first RF waveform by−2nπ/γG.
 10. The system of claim 9, wherein RF pulses are emitted intothe object by n RF coil elements.
 11. The system of claim 10, whereinn≧3.
 12. The system of claim 9, wherein the first, second and third RFwaveforms are substantially identical in shape.
 13. The system of claim9, further comprising a receive module configured to, after the third RFpulse is emitted, detect an RF signal scattered from the object forgenerating an MRI image.
 14. The system of claim 9, wherein the first RFexcitation coil element has a first sensitivity profile comprising afirst phase that is substantially constant in a direction across animaging volume of the object, the second RF excitation coil element hasa second sensitivity profile comprising a second phase that variessubstantially linearly, with an n multiple of 2π, in the directionacross the imaging volume, and the third RF excitation coil element hasa third sensitivity profile comprising a third phase that variessubstantially linearly, with an n multiple of −2π, in the directionacross the imaging volume.
 15. The system of claim 14, wherein the firstphase is substantially zero across the imaging volume.
 16. The system ofclaim 14, wherein the sensitivity profile of each of the first, secondand third excitation coil elements comprises a substantially uniformamplitude across the imaging volume.
 17. A method, of emitting radiofrequency (RF) pulses into an object during magnetic resonance imaging(MRI), comprising: emitting a first RF pulse into the object with afirst RF excitation coil element, wherein the first RF pulse comprises afirst RF waveform; emitting a second RF pulse into the object with asecond RF excitation coil element, wherein the second RF pulse comprisesa second RF waveform that is time shifted relative to the first RFwaveform by 2nπ cos θ/γG, where θ is an angle between a selected sliceand an axial plane, G is a gradient strength of a slice-select gradient,γ is a gyromagnetic ratio in units of radians per unit gradientstrength, and n is an integer; and emitting a third RF pulse into theobject with a third RF excitation coil element, wherein the third RFpulse comprises a third RF waveform that is time shifted relative to thefirst RF waveform by −2nπ cos θ/γG.
 18. The method of claim 17, whereinthe first, second and third RF waveforms are substantially identical inshape.
 19. The method of claim 17, further comprising, after emittingthe third RF pulse, detecting an RF signal scattered from the object forgenerating an MRI image.
 20. The method of claim 17, wherein the firstRF excitation coil element has a first sensitivity profile comprising afirst phase that is substantially constant in a direction across animaging volume of the object, the second RF excitation coil element hasa second sensitivity profile comprising a second phase that variessubstantially linearly, with an n multiple of 2π, in the directionacross the imaging volume, and the third RF excitation coil element hasa third sensitivity profile comprising a third phase that variessubstantially linearly, with an n multiple of −2π, in the directionacross the imaging volume.